1. Field of the Invention
The present invention relates to an optical imaging system used in an image transmission portion of, e.g., a facsimile device or a copier. More particularly, the present invention relates to an optical imaging system including a plurality of rod lenses arranged in an array.
2. Description of the Related Art
Optical imaging systems including a plurality of rod lenses with a refractive index distribution in the radial direction that are arranged in an array are widely used in the image transmission portion of, e.g., facsimile devices or copiers.
The refractive index distribution of such rod lenses can be expressed, e.g., byn(r)2=n02·{1−(g·r)2+h4·(g·r)4+h6·(g·r)6+h8·(g·r)8}  Eq. 6where r is a radial distance from the optical axis of the rod lens, n(r) is a refractive index at the radial distance r, n0 is a refractive index on the optical axis of the rod lens (i.e., the center refractive index), and g, h4, h6 and h8 are refractive index distribution coefficients.
Conventionally, the resolving power demanded from such a rod lens array called for an MTF (modulation transfer function) of at least 60% when a pattern of 4–6 line-pairs/mm (ca. 200 dpi–300 dpi) was imaged. To meet this demand, it was sufficient to control only g or both g and h4 of the refractive index distribution coefficients for the rod lenses.
Recently, however, with the steadily rising quality of printers and scanners, there is a demand for rod lens arrays with a resolving power of at least 12 line-pairs/mm (ca. 600 dpi). To achieve a rod lens array having such a high resolving power, all the refractive index distribution coefficients, including h6 and h8, have to be controlled precisely during design and fabrication of the rod lens array.
It is possible to determine the optimum refractive index distribution coefficients for correcting the spherical aberration on the optical axis of a single rod lens. However, in the case of a plurality of rod lenses arranged in an array, a change in the resolving power may be caused not only by the spherical aberration, field curvature and astigmatism of the individual lenses but also by the overlapping of images from neighboring lenses.
The optimum refractive index distribution also changes depending on the brightness of the rod lenses. For example, when bright rod lenses having a large angular aperture are employed, the refractive index distribution coefficients for a small axial spherical aberration are very different from the refractive index distribution coefficients for a small field curvature. The best resolving power can be achieved by striking a balance between the two.
An overlapping degree m is given bym=X0/2r0  Eq. 7where r0 is the radius of an effective lens portion, i.e., the radius of the portion of each rod lens that functions as a lens, and X0 is the image radius that a single rod lens projects onto an image plane (i.e., the field of view). Here, X0 is defined as X0=−r0/cos (Z0π/P), where Z0 is the length of a rod lens and P is a one-pitch length of the rod lens. Even if the rod lenses have the same refractive index distribution, the overlapping degree m changes with the lens length, and thus causing a change in the resolving power.
Consequently, to achieve a high resolving power, the refractive index distribution coefficients have to be determined separately in accordance with at least the brightness and the overlapping degree of each rod lens.